Yes some people's beliefs are based on misinterpretation of the facts. The problem is we don't really know whose views are wrong and whose are right and we may never know. Many people change the facts and the ideas to make them fit into their own way of thinking rather than accepting the facts.
I have heard countless arguments for young earth creationism and so far for me every single bit of evidence for it has been wrong or based on a fallacy. An example of this would be "We have found fossilised thorns along with dinosaur bones and because God created the thorns 6000 years ago dinosaurs must have lived then" or "If the world was millions of years old you would expect to find millions of fossils but if the world is only thousands of years old you would expect to find thousands like we have"
To me that demonstrates no more than a misunderstanding of the fields of information that they are related to. I am of the persuasion that there is NO concrete empirical evidence for y.E.C. And that any evidence that has been found can be attributed to an incomplete understanding of what they are trying to refute/prove.
Old earth creationists have a belief that every thing must be as it seems, that we must look at the evidence the earth is giving us. But new earth creationists realise that if God has the power to create the Universe, the earth and humans then he can pretty much do anything. What is to stop him from having created the earth in such a way that to us the evidence seems like it has been around much longer than it has.
I used to be a Young Earth Creationist. It had nothing to do with the scientific evidence, but how I read the Bible. What changed my mind? No evidence changed my mind, but I realized I was reading Scripture incorrectly. The way I was reading it was not the way the author intended it to be understood.
It's not based on a misinterpretation or misunderstanding of the facts, it's based on a choice to ignore the facts that are known. Most of them know the facts that science has discovered on the age of the earth but chose to ignore those facts. They don't misinterpret anything, they just ignore facts.